Answer:
1022 minutes
Step-by-step explanation:
Let x be the number of minutes the executive used the phone
There is a base charge of $35 and only minutes greater than 900 min are charged at the rate of $0.40 per minute
So total bill A = 35 + 0.4(x-900)
We know the bill was $83.80
So we can rewrite the equation as
35 + 0.4(x-900) = 83.30
and solve for x
To make it easier for computational purposes
1) Multiply both sides by 10
[tex]35\cdot \:10+0.4\left(x-900\right)\cdot \:10=83.8\cdot \:10[/tex]
2) Perform individual multiplication
[tex]350+4\left(x-900\right)=838[/tex]
3) Subtract 350 from both sides
[tex]350+4\left(x-900\right)-350=838-350[/tex]
4) Simplify
[tex]4\left(x-900\right)=488[/tex]
5) Divide both sides by 4
[tex]\frac{4\left(x-900\right)}{4}=\frac{488}{4}[/tex]
6) Simplify
[tex]x-900=122[/tex]
7) Add 900 to both sides to isolate x
[tex]x-900+900=122+900[/tex]
8) Simplify to obtain x
[tex]x=1022[/tex]
Answer: The executive used the phone for 1022 minutes that month
Perform the indicated operation & simplify. Express the answer as a complex number. ( 12 − 11 i ) 2
The answer is 24 - 22i
The answer we got is a complex number.
We are asked to find out the multiplication of a complex number and a real number.
The general form of a complex number is a + bi.
If we need to find the product of a complex number and a real number,
then, we need to multiply the real and imaginary parts by the real number and write down the answer.
The real number given is 2.
And the complex number given is 12 - 11i.
The real part of the complex number is 12.
And the imaginary part of the complex number is -11.
When the real part of the complex number is multiplied by the real number, we get 12 × 2 = 24.
When the imaginary part of the complex number is multiplied by the real number, we get (-11) × 2 = -22
Therefore, the required complex number is 24 - 22i
Learn more at:
https://brainly.com/question/26125074
#SPJ9
Determine if each statement is TRUE or FALSE.
15. LAGF and LBGE are vertical angles..
Answer:
TRUE
Step-by-step explanation:
na sa inyo na answer
Answer:
Add your questions
Step-by-step explanation:
Rs=3x st=6x-5 rt=58 find st
The value of st is 30.4
As S is the point in RT, it implies that RS+st=Rt. Therefore according to the question,
3x+6x-5=58
⟹9x=58-5
or
9x=53
⟹x=5.9
RS = 3×5.9=17.7
st=(6×5.9)-5=35.4-5=30.4
Learn more about finding values here:
https://brainly.com/question/5685820
#SPJ9
The Lopez family buys 4 dinners at the market. The total cost is $5 above or below $50. Write an equation that models the cost x, in dollars of a single dinner?
answer: |_-_x|-_=0
==================================================
Explanation:
x = cost of one dinner
4x = cost of four dinners
50-4x = the difference in the cost of $50 vs 4x dollars
To ensure this difference is never negative, we use absolute value to form the expression |50-4x|
Set this equal to 5 since we want this distance or difference to be 5 units above or below 50
|50-4x| = 5
|50 - 4x| - 5 = 0
Answer:
l 50 - 4x l - 5 = 0
Step-by-step explanation:
Graph the numbers -0.2, 7/10, -1, √2, and -4 on a number line.
-8 -7, -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Answer:
Step-by-step explanation:
-3x+6=-24bwhat is the value of 2x-17
The value of the expression 2x - 17 is 3
How to evaluate the expression?The expression is given as
-3x + 6 = -24
Subtract 6 from both sides
-3x = -30
Divide both sides by -3
x = 10
Multiply by 2
2x = 20
Subtract 17 from the sides
2x - 17 = 3
Hence, the value of the expression 2x - 17 is 3
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
You are buying a new car. There are 7 body styles, 3 colors, and 7 models. How many different choices of car are there?
Answer:
147 different choices.
Step-by-step explanation:
(7)(3)(7) = 147
Hope this helps
There are 8 adults in line for a ride. The line has 4 fewer children than adults. How many people are in line? Explain your answer.
Answer:
12 People
Step-by-step explanation:
To start you have 8 people for sure. Then you know that there are 4 fewer children. So then you subtract 4 from 8 and get four. Four plus eight is twelve!
The number of people in line will be 12.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
There are 8 adults in line for a ride. The line has 4 fewer children than adults. Then the number of children will be
⇒ 8 - 4
⇒ 4 children
Then the number of people in line will be
⇒ 8 + 4
⇒ 12
The number of people in line will be 12.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Which inequality does this graph match?
−19 + 7k< −6(−4−k)
−7 (4−x) + 4 > −18 + 7x
−4 (4+7x) + x < −6x + 5
−2n − 40 < 5 (6+n) + 7n
Answer:
I think it is -5
Step-by-step explanation:
Help me with this problem please
Last year, Abdul opened an investment account with $8600. At the end of the year, the amount in the account had decreased by 7.5%. How much is this decrease in dollars? How much money was in his account at the end of last year?
The amount that decreased in dollars is equal to $ 645 and the money left in the account at the end of the year is $ 7955.
The amount of investment that Abdul opened an account with = $ 8600
The amount decreased by 7.5 %.
So, the amount left will be calculated by first using the percentage to find the amount that decreased.
Amount decreased = 7.5 % of 8600
Amount decreased = 0.075 × 8600
Amount decreased = $ 645
Amount left at the end of the year = $ 8600 - $ 645
Amount left at the end of the year = $ 7955
Therefore, the amount that decreased in dollars is equal to $ 645 and the money left in the account at the end of the year is $ 7955.
Learn more about percentage here:
https://brainly.com/question/843074
#SPJ9
HELP ASAP I WILL GIVE 30 points to whoever can show their work!
Answer:
Step-by-step explanation:
sin(A)=2/5
[tex]cos^2(A) +sin^2(A)=1\\cos^2(A)+[\frac{2}{5}]^2=1\\cos^2(A)+\frac{4}{25}=1\\ cos^2(A)=1-\frac{4}{25}\\ cos^2(A)=\frac{21}{25}\\ cosA=\frac{\sqrt{21} }{5}[/tex]
step by step explanation
The sum of the given infinite geometric series is; 32
What is the sum of the geometric series?The general formula for finding the sum of an infinite geometric series is s = a₁/(1 - r)
where;
s is the sum
a₁ is the first term of the series
r is the common ratio.
To find the common ratio, use the formula: r = a2⁄a1
where a2 is the second term in the series and a1 is the first term in the series.
Thus;
r = 2²/4²
r = 1/2
Thus;
S = 4²/(1 - 1/2)
S = 16/(1/2)
S = 32
Read more about Sum of Geometric Series at; https://brainly.com/question/24643676
#SPJ1
Help, I don’t know how to solve this
Answer:
a=A/8
Step-by-step explanation:
This MIGHT be the answer, I am 99% sure!
Find the perimeter of the rectangle. Then, find the area of the rectangle. Round your
answer to the nearest tenth, if necessary.
(Lesson 2-3)
Solution :
solve by considering data :
The perimeter of a rectangular pool is 56 meters. If the length of the pool is 16 meters, then find its width.
Here the perimeter and the length of the rectangular pool are given. We have to find the width of the pool.
The perimeter P of a rectangle is given by the formula, P=2l+2w, where l is the length and w is the width of the rectangle.
Given that, the perimeter is 56 meters and the length is 16 meters. So, substitute these values into the formula.
56=2(16)+2w
Simplify.
56=32+2w
Subtract 32 from both sides.
24=2w
Divide each side by 2 .
12=w
Therefore, the width of the rectangular pool is 12 meters.
More details: brainly.com/question/15019502
#SPJ9
A large water container has a leak. It loses 40 drops of water every minute. If 50 drops of water is equivalent to half of a teaspoon. At what rate
Is the water leaking?
O 48 teaspoons per hour
24 teaspoons per hour
O 80 teaspoons per hour
O 12 teaspoons per hour
O 20 teaspoons per hour
The student council is selling popsicles to raise money for prom. Each box contains 10
popsicles and each box costs $4.50. How much does the school need to charge per
popsicle to make a profit of $6 per box?
Answer:
1.05 dollars per popsicle
Step-by-step explanation:
x is the price per popsicle. In order for you to make 6 dollars of profit, each box is going to cost 10.50 dollars because 4.50 is your amount of expenses.
Profie= revenue-expenses
6= revenue-4.5
revenue=10.5
If you charge 10.5 per box, and each box has 10 popsicles, then one popsicle is 10.5/10=1.05 dollars per popsicle.
Help me plsss this is my last oneeeree
Answer:
For the first question:
The fraction that comes after 0/3 is 1/3The fraction that comes after 1/3 is 2/3For the second question:
The fraction that comes after 0/6 is 1/6The fraction that comes after 1/6 is 2/6The fraction that comes after 2/6 is 3/6The fraction that comes after 3/6 is 4/6The fraction that comes after 4/6 is 5/6Step-by-step explanation:
Hope it helps! =D
Find the slope of the line if it exists.
The slope of the line is 1.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount
To calculate the slope of the graph, we use the formula below.
Formula:
Slope (S) = (y₂-y₁)/(x₂-x₁)............ Equation 1From the question,
Given:
y₁ = 0y₂ = 4x₁ = -6x₂ = -2Substitute these values into equation 1
S = (4-0)/[-2-(-6)]S = 4/4S = 1Hence, the slope of the line is 1.
Learn more about slope here: https://brainly.com/question/3493733
#SPJ1
Roy has $253.97 in his bank account. He loans his friend $81.19. How much money does he have in his
account?
Answer:
172.78
Step-by-step explanation:
Simplify the expression √48
Financial Goals: Tutorial
Part C
? Question
Diego's cash flow is the difference of his monthly income, $3,000, and his total expenses, $2,715. Which equation
correctly represents Diego's cash flow?
O cash flow = $2,715 - $3,000
O cash flow = $3,000-$2,715
O $3,000 = $2,715 - cash flow
$3,000 = cash flow-$2,715
Submit
25 of 37 Save & Exit
Σ
Sign out
Sep 6
7:56
The equation that represents Diego's cash flow is cash flow = $3,000-$2,715.
What is the cash flow?Cash flow is the difference between cash inflows and cash outflows. Cash inflow are additions to the cash flow. An example of cash inflow is monthly income. Cash outflow would reduce the cash flow. An example of cash inflow is expenses.
Cash inflow = income - expense
$3,000 - $2,715
To learn more about cash flows, please check: https://brainly.com/question/28238360
#SPJ1
PLEASE HELP ME. DUETODAY. NEED ANSWER ASAP!!!!!!
Answer: 120 ==> scale
8.4 m==> longer side
Step-by-step explanation:
6 m=
6*100 cm=600 cm
600/5=120 ==> scale
7*120=840 cm
840 cm=
840/100 m=8.4 m ==> longer side
A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the two stations. How many bicycles are at the Main Street station?
There are 20 bicycles at the Main Street station.
According to question statement, A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the given two stations.
We are supposed to know the number of bicycles at the Main Street station.
Let us assume that the number of bicycles at the Park Avenue station is "x". Then, number of bicycles at the Main Street station will be "5x".
We will have to form a Linear Equation of single variable "x" as per the conditions based in the question statement, and solving for x, we will obtain our desired answer.
As there are 24 bicycles at the two stations therefore,
[tex]x + 5x = 24[/tex], will be our equation.
Solving the equation for x, we get
[tex]x + 5x = 24\\6x = 24\\x=\frac{24}{6} \\or x=4[/tex]
Therefore the number of bicycles at the Park Avenue station is 4.
And the number of bicycles at the Main Street station will be 5x i.e., [tex]5*4 = 20[/tex].
Linear Equation: The equation whose graph is always a straight line.To learn more about linear equations, click the link given below
https://brainly.com/question/11897796
#SPJ9
find the average of 1/8, 1/6, and 3/4
Answer:
Average= [tex]\frac{25}{72}[/tex]
Step-by-step explanation:
o find the average add up the values and divide the sum by the number of values.
Rewriting all values as fractions, rewriting any negatives if necessary and, setting up as an addition problem
= [tex]\frac{1}{8}[/tex] + [tex]\frac{1}{6}[/tex] +[tex]\frac{3}{4}[/tex]The least common denominator (LCD) is: 24.
Rewriting as equivalent fractions with the LCD:
= [tex]\frac{3}{24\\}[/tex] + [tex]\frac{4}{24}[/tex] + [tex]\frac{18}{24}[/tex]Rewriting numerators over the common denominator,
= [tex]\frac{3 + 4 + 18}{24}[/tex]Totaling the numerator:
= [tex]\frac{25}{24}[/tex]
Dividing by the number of values: 3
[tex]\frac{25}{24}[/tex] ÷3 =[tex]\frac{25}{24}[/tex] ×[tex]\frac{1}{3}[/tex] = [tex]\frac{25}{72}[/tex]
Average of the fractions is:
Average= [tex]\frac{25}{72}[/tex]
Mia has 7 boxes of cherry tarts. Each box has 8 cherry tarts. Explain how to use an open number line to solve.
Use of open number line is
7 boxes of cherry tarts
Each box has 8 cherry tarts.
Total cheny tarts is
[tex]$$7 \times 8=7+7+7+7+7+7+7+7$$[/tex]
A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and drop as we move to the left.
A number line is a visual depiction of numbers on a straight line drawn either horizontally or vertically. It is simple for humans to compare numbers and carry out simple arithmetic operations on them when they are written down on a number line. A number line is said to begin at zero (0). Left of zero, there are only negative numbers, and right of zero, there are only positive numbers. So, on a number line, we may say that the value of numbers grows as we travel to the right. This indicates that there are more numbers on the right than on the left.
To learn more about number line visit: https://brainly.com/question/7352552
#SPJ9
Brainliest, 5 star, & thanks.
The coordinates of the vertices of △PQR are P(4, −2) , Q(6, −4) , and R(8, 0) .
The coordinates of the vertices of △P′Q′R′ are P′(−4, 3) , Q′(−6, 5) , and R′(−8, 1) .
Sixty-three and six-teen-thousandths
Answer:
63 and 16,000
Step-by-step explanation:
Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each. How many containers can she fill?
Answer: 10
Step-by-step explanation: First you decide that each container can fill 3/4 of a cup. You have 8 cups so you need to divide 8 by 3/4 which will give you the answer of 10.666 repeating so the answer is you can only fill up 10 containers.
Which sequence of transformations on preimage ∆ABC will NOT produce the image ∆A'B'C'?
Graph shows 2 triangles plotted on a coordinate plane. First triangle is at A(minus 3, 0), B(minus 2, 3), C(minus 1, 1). Second triangle is at A prime (0, minus 3), B prime (3, minus 2), C prime (1, minus 1).
A.
reflection across the line y = x
B.
reflection across the x-axis followed by a reflection across the y-axis
C.
reflection across the line y = -x followed by a rotation 180° counterclockwise about the origin
D.
reflection across the y-axis followed by a rotation 90° clockwise about the origin
E.
rotation 180° clockwise about the origin followed by a reflection across the line y = -x
The geometric transformation which will not produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis
In this question, we have been given a triangle ABC and the transformed triangle A'B'C'
Also, in the graph the first triangle is at A(-3, 0), B(-2, 3), C(- 1, 1) and the Second triangle is at A prime (0, -3), B prime (3, -2), C prime (1, -1).
Consider the graph as shown below.
From the coordinates of vertex of triangle ABC and triangle A'B'C' we can observe that,
A(-3, 0) -> A'(0, -3)
B(-2, 3) -> B'(3, -2)
C(-1, 1) -> C'(1, -1)
For each vertex,
x coordinate of triangle ABC = y coordinate of triangle A'B'C'
and y coordinate of triangle ABC = x coordinate of triangle A'B'C'
This means, the geometric transformation of triangle ABC is reflection across the line y = x
But the reflection across the x-axis followed by a reflection across the y-axis.
Therefore, the geometric transformation which will not produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis
Learn more about the transformation here:
https://brainly.com/question/14043032
#SPJ1
